Coupled-generalized nonlinear Schr¨odinger equations solved by adaptive step-size methods in interaction picture  

作　　者：陈磊 李磐 刘河山 余锦 柯常军 罗子人 Lei Chen;Pan Li;He-Shan Liu;Jin Yu;Chang-Jun Ke;Zi-Ren Luo(Aerospace Information Research Institute,Chinese Academy of Sciences,Beijing 100094,China;National Microgravity Laboratory,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]Aerospace Information Research Institute,Chinese Academy of Sciences,Beijing 100094,China [2]National Microgravity Laboratory,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China [3]University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Chinese Physics B》2023年第2期332-340,共9页中国物理B（英文版）

基　　金：supported by the National Key Research and Development Program of China (Grant Nos. 2021YFC2201803 and 2020YFC2200104)。

摘　　要：We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(RK4IP-CQE), and the other is the local error adaptive step-control method(RK4IP-LEM). The methods are developed in the vector form of fourthorder Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.

关 键 词：nonlinear optics optical propagation in nonlinear media coupled-generalized nonlinear Schr?dinger equations(C-GNLSE) adaptive step-size methods 

分 类 号：O175.29[理学—数学]